Revision as of 17:23, 7 October 2008 by Bchanyas (Talk)

The formula of the inverse transform is:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \, $

Suppose we have $ 2 \pi \delta(w - 2\pi) $ (From the 'not so easy' question in class)

Substituting that into the formula:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = e^{j2 \pi t}\, $

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood